McL 151 Assign 3

# McL 151 Assign 3 - any non-singular square matrix. [3...

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1 SCORE : /25 NAME : ___________________________ STUDENT NUMBER : _______________ Math 151 A03 & A04 Assignment #3 DUE: WEDNESDAY, MARCH 10 th , 2010 At the START of CLASS – NO EXCEPTIONS ! *** UNSTAPLED ASSIGNMENTS WILL NOT BE ACCEPTED*** ANSWERS ALONE WILL EARN YOU NO CREDIT. ALL RELEVANT WORKINGS MUST BE SHOWN IN FULL. COMPLETE EACH QUESTION AS IF YOU WERE PRESENTING YOUR SOLUTION IN THE CONTEXT of an EXAM. ------------------------------------------------------------------------------------------------------------------------------ 1. Solve the following system using Gauss-Jordan Elimination. [5 Marks] 3 x 1 + 2 x 2 + 12 x 3 + 2 x 4 + 15 x 5 + 14 x 6 = 13 2 x 1 + x 2 + 7 x 3 + x 4 + 9 x 5 + 8 x 6 = 7 2 x 1 + 2 x 2 + 10 x 3 + 3 x 4 + 14 x 5 + 15 x 6 = 15

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2 2. A, B and C are matrices defined as follows: A = 1 3 1 2 1 1 È Î Í ˘ ˚ ˙ B = - 1 1 0 - 1 1 0 È Î Í Í Í ˘ ˚ ˙ ˙ ˙ C = 2 3 3 5 È Î Í ˘ ˚ ˙ a) Solve the following matrix equation for the matrix D. [2 Marks] AB - 1 2 CD = 0 b) What size is matrix D? [1 Mark] c) Find the inverse of C using the method which can be used to find the inverse of

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Unformatted text preview: any non-singular square matrix. [3 Marks] d) Find matrix D. [2 Marks] 3 3. Define matrices X and T as follows: X = x 1 x 2 x 3 [ ] T = 0.6 0.3 0.1 0.4 0.3 0.3 0.3 0.3 0.4 È Î Í Í Í ˘ ˚ ˙ ˙ ˙ You will find the values of x 1 , x 2 , x 3 which satisfy X = XT and x 1 + x 2 + x 3 = 1 through the following steps: a) From the matrix equation X = XT, find three linear equations involving x 1 , x 2 , x 3 . [3 Marks] b) Your three equations in part (a) above, plus the equation x 1 + x 2 + x 3 = 1 together form a system of four equations. Solve this system for x 1 , x 2 , x 3 using the Gauss-Jordan elimination method. [4 Marks] 4 4. Suppose some experiment has events A, B, and C, and that: i) P(B) = 0.4 ii) P(C) = 0.5 iii) P(A|B) = 0.25 iv) P(B|C) = 0.5 v) P(A|C) = 0.4 vi) P(AUB) = 0.6 vii) P(A « B « C) = 0.05 Find the probability that exactly one of A, B or C occurs. [5 Marks]...
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## This note was uploaded on 01/15/2011 for the course MATH 151 taught by Professor Barone during the Spring '09 term at University of Victoria.

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McL 151 Assign 3 - any non-singular square matrix. [3...

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